Solve 3x^3*(-x)

$$3 { x }^{ 3 } \times (-x)$$

Evaluate

$$-3x^{4}$$

Solution Steps

Multiply 3 and -1 to get -3.

$$-3x^{3}x$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-3x^{4}$$

Differentiate w.r.t. x

$$-12x^{3}$$

Steps Using Definition of a Derivative

Multiply 3 and -1 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{3}x)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4\left(-3\right)x^{4-1}$$

Multiply 4 times -3.

$$-12x^{4-1}$$

Subtract 1 from 4.

$$-12x^{3}$$